My preliminary idea is a "fuel bladder" for take-off that inflates with enough fuel to get the plane to a recoverable altitude, maybe a few thousand feet?

Or maybe a design that prevents both switches being off (flip flop?) for X minutes after wheel weight is removed?

Again, it’s probably pointless but it’s an interesting thought exercise.

Suicidal pilots are apparently more common than we’d want.

There’s always going to be many ways they could crash the plane, such a feature wouldn’t help. The pilots are the only people you can’t avoid fully trusting on the plane.

There's a balance of accidents to be found, I think. There are likely cases where fuel does need to be cut off to both engines, and preventing that would lead to accidents that might have been recoverable. This case shows that cutting off fuel to both engines during takeoff is likely unrecoverable. There have been cases where fuel is cutoff to the wrong engine, leading to accidents. Status quo might be the right answer, too.

Formally verified traditional algorithms.

Coming up with ad-hoc solutions is easy, especially the less you know about a complex system and its constraints. I'd say it's not an interesting exercise unless you consider why a solution might not exist already, and what its trade-offs and failure modes are. Otherwise, all you're doing is throwing pudding against a wall, which can of course be fun.

For example, an obvious solution is that the switch can't be changed from "RUN" to "CUTOFF" when the throttle isn't at idle - this could be done with a mechanical detent because they're right next to each other. Simple!

But now you've introduced additional failure modes - throttle sticks wide open and the engine is vibrating and needs to be shut down - so maybe you make it that the shutdown switch can work for ONE engine at any throttle position, but if TWO get turned off, both throttles have to be off, but that introduces ...

If there’s a fire or similar problem the fire handles will cut off fuel without the normal shutdown procedure, but the normal switches only need to be used at idle thrust.

I wonder if Airbus has this logic, since their philosophy is to override the pilot commands if they’d endanger the aircraft (which has its own issues of course) where’s Boeing will alert the pilots and still perform the action. I don’t have access to that information.

As another commenter said the Airbus engine start/stop controls are located behind the thrust levers, and according to the A350 operations manual which I got my hands on there are two conditions required for the FADEC to command engine shut down: Run switch to off, thrust lever to idle.

So if that's correct on an Airbus aircraft you can't just switch off the engines when they're commanded to produce thrust. This also seems to be backed up by the difference in the guards for those controls in the Airbus cockpits.

Will the bladder be marketed by Kramerica Industries?

Why would anyone risk potentially surviving a sabotage like that ?

The wings hosts the engine and a good portion of the fuel is quite a bit back from the nose in a big plane like 787. The engines lost power and hit just 180 knots just 4 seconds after the plan lifted off. The plane could have just easily broken up differently where the nose crashed in a different spot than where the fire would likely start.

At such a slow speed and altitude they could even have well crashed inside the airport perimeter and got a quicker/ better emergency response from the fire units at the airport.

Attempting this during takeoff or landing when the pilot monitoring is fully engaged and closely observing would be most difficult to execute .